Earlier in the day, the weather office had said the start of the monsoon would be on May 31.
The latest weather forecast showed that southwesterly winds could strengthen further gradually from June 1, resulting in a likely enhancement in rainfall over the southern state of Kerala, the forecast said.
"Hence the monsoon onset over Kerala is likely to take place by 3rd June 2021," it said.
Nearly half of India's farmland has no irrigation and depends on annual June-September rains to grow crops such as rice, corn, cane, cotton and soybeans.
India's weather office said last month the country was expected to get average monsoon rains this year, raising expectations of higher farm output, which is central to the country's economy.
(Reporting by Mayank Bhardwaj and Swati Bhat; Editing by Kim Coghill and Jane Merriman)